You are in Camelot, sipping an ale and having a crumpet, whatever those are. You decide to move to the Grail Quest. Thankfully, the travel deck allows you to make it to the quest. Merlin was already at the quest so was there when you got there.

The question is, can you now draw an extra card since you got to the quest on this turn and Merlin was there? Or, can you only draw an extra card if you are at the quest and Merlin was at the quest at the start of your turn?

Similar scenario is that you move to a quest, you get a Merlin travels card, can you then draw an extra white card since you get to the quest with Merlin?

Unless we've been playing it wrong, you get an extra card from Merlin simply because you are on a quest where he is.

The rules read,
"Once during each player's turn, when his Knight is
present on the same Quest as Merlin, the player may
choose to draw a White card from the draw pile. This
draw is a free Action and does not count toward the
Knight's Heroic Action(s) for the turn."